Must Be True Classification

Must Be True Classification problems present a set of premises followed by statements that need to be classified as 'Must be true', 'Could be true', or 'Must be false' based on the given information. These problems test your ability to distinguish between necessary, possible, and impossible conclusions.

10Worksheets
200+Practice Questions
HardDifficulty
3-4 hoursHours to Master

Introduction to Must Be True Classification

Must Be True Classification problems present a set of premises followed by statements that need to be classified as 'Must be true', 'Could be true', or 'Must be false' based on the given information. These problems test your ability to distinguish between necessary, possible, and impossible conclusions.

Prerequisites

Understanding of logical necessity vs possibility Knowledge of logical impossibility Venn diagram reasoning Contrapositive reasoning
Why This Matters: Must Be True Classification problems appear in 1-2 questions in advanced exams. They test nuanced logical discrimination skills.

How to Solve Must Be True Classification Problems

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Step 1: Analyze the premises and understand what they establish

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Step 2: For each statement to classify, ask three questions

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Step 3: 'Must be true' - Is the statement true in every possible scenario consistent with the premises?

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Step 4: 'Could be true' - Is there at least one scenario where the statement is true?

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Step 5: 'Must be false' - Is the statement false in every possible scenario?

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Step 6: Use Venn diagrams to test different possible configurations

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Step 7: Classify each statement accordingly

Pro Strategy: Use the contrapositive: If P→Q, then ¬Q→¬P. Remember that P→Q does NOT imply Q→P. To determine 'Must be false', check if the statement contradicts the premises or their contrapositives. To determine 'Could be true', find at least one consistent scenario where the statement holds.

Example Problem

Example: Premises: 'All students who passed the exam studied at least 10 hours. John studied 15 hours. Mary studied 5 hours. Sarah studied 10 hours exactly.' Classify: 'John passed the exam' Solution: Step 1: Premise: Passed → studied ≥ 10 hours (contrapositive: studied < 10 hours → did not pass) Step 2: John studied 15 hours (≥ 10) Step 3: Does this guarantee John passed? No - the premise says if passed then studied ≥10, not that studying ≥10 guarantees passing Step 4: John could have passed or failed (both are possible) Step 5: Therefore, 'John passed' is possible but not necessary Answer: Could be true

Pro Tips & Tricks

  • 'Must be true' = statement holds in all possible worlds consistent with premises
  • 'Could be true' = statement holds in at least one consistent world
  • 'Must be false' = statement holds in no consistent world (contradicts premises)
  • The contrapositive of a true statement is also true
  • The converse and inverse are not necessarily true
  • Use Venn diagrams to test multiple possibilities

Shortcut Methods to Solve Faster

If P→Q and P is given → Q must be true
If P→Q and ¬Q is given → ¬P must be true
If P→Q and Q is given → P could be true (not must)
If P→Q and ¬P is given → nothing certain about Q

Common Mistakes to Avoid

Confusing 'could be true' with 'must be true'
Assuming the converse of a conditional is valid
Thinking that if something is possible, it's necessarily true
Forgetting to test multiple scenarios before concluding 'must be true'

Exam Importance

Must Be True Classification is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
2-3 questions
INSURANCE
1-2 questions

Ready to Master Must Be True Classification?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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